The scripts linked at /etc/rc0...6.d/ have numbers at the begining right after the letter S/K, so the question is what is order of execution? From the lower to higher or higher to lower? I also would like to know if there is any rules on these number, can I create a script with number 1, 2, ..., 97, 98, or only some specific numbers are allowed?

I'd like to run a script after the system boot and before the system shutdown, but as those scripts needs internet connection to perform its tasks at which runlevel folder should I place it?